Extrude vertices along edges
Three different ways to do this currently. Options #1 and #2 only allow to specify distance factors relative to edge length. Option #3 should allow absolute units.


Use vertex slide: Press G,G twice to activate Vertex Slide, while the cursor is hovering the edge with the desired direction. Afterwards press C to deactivate clamping and allow extending beyond current position.





Scale in relation to the other vertex: Place you 3D cursor at the other end of the edge by snapping it to the vertex with Shift+S > Cursor to Selected. Change the Transform Pivot to the 3D Cursor and then scale the opposing vertex with S.





Use a custom transform Orientation: Select the edge with the desired direction. In the 3D View Properties Area from Transform orientations chango to local and press + to add a new one. Select it from the list (should be named Edgeby default), then select your vertex and move it by using G then tapping twice the desired axis to move in local coordinates, in this case Y,Y.